Multisymplectic geometry and multisymplectic Preissmann scheme for the KdV equation

Journal of Physics A: Mathematical and General

Volumn 33, Issue 18, 2000, Pages 3613-3626

  Zhao, Ping Fu ^a,b   Qin, Meng Zhao ^a,b  

^a CCAST WORLD LABORATORY   (China)

^b INSTITUTE OF GEOLOGY AND GEOPHYSICS   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034640067     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/33/18/308     Document Type: Article

References (17)

1. Feng K and Qin M Z 1987 The symplectic methods for computation of Hamiltonian systems Proc. Conf. on Numerical Methods for PDEs (Lecture Notes in Mathematics vol 1297) ed Y L Zhu and Guo Ben-Yu (Berlin: Springer) pp 1-37
2. Li C W and Qin M Z 1988 A symplectic difference scheme for infinite dimensional Hamiltonian systems J. Comput. Math. 6 164-74
3. Qin M Z 1997 A symplectic difference scheme for the PDEs AMS/IP Studies in Advanced Mathematics vol 3, pp 349-54
4. Qin M Z 1990 Multi-stage symplectic schemes of two kinds of Hamiltonian systems of wave equations Comput. Math. Appl. 19 51-62
5. Qin M Z and Zhu W J 1993 Construction of symplectic schemes for wave equation via hyperbolic functions sinh(x), cosh(x) and tanh(x) Comput. Math. Appl. 26 1-11
6. McLachlan R 1994 Symplectic integration of Hamiltonian wave equations Numer. Math. 66 465-92
7. Marsden J E and Shkoller S 1999 Multisymplectic geometry, covariant Hamiltonians, and water waves Math. Proc. Camb. Phil. Soc. 125
8. Marsden J E, Patrick G P and Shkoller S 1998 Multisymplectic geometry, variational integrators, and nonlinear PDEs Commun. Math. Phys. 199 351-95
9. Gotay MJA Multisymplectic approach to the KdV equation Differential Geometrcal Methods in Theoretical Physics (NATO Advanced Science Institute Series C: Mathematical and Physical Sciences vol 250) ed K Bleuler and M Werner pp 295-305
10. Bridges T J 1997 Multisymplectic structures and wave propagation Math. Proc. Camb. Phil. Soc. 121
11. Bridges T J and Derks G 1999 Unstable eigenvalues and the linerization about solitary waves and fronts with symmetry Proc. R. Soc. A 455 2427-69
12. Reich S 2000 Multi-symplectic Runge-Kutta methods for Hamiltonian wave equations J. Chem. Phys. 157 473-99
13. Bridges T J and Reich S 1999 Multisymplectic integrators: numerical schemes for Hamiltonian PDEs that conserve symplecticity Preprint Department of Mathematics and Statistics, University of Surrey
14. Drazin P G and Johnson R S 1989 Solitons: an Introduction (Cambridge: Cambridge University Press)
15. Zabusky N J and Kruskal M D 1965 Phys. Rev. Lett. 15 240
16. Olver P J 1986 Applications of Lie Groups to Differential Equations (New York: Springer)
17. Abbott M B and Basco D R 1989 Computational Fluid Dynamics (London: Longman Scientific)